Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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Write_Mikey_Write!

about 23 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

December 18, 2019 at 12:02am

#971632

Red Queen's Race

While we're on the subject of weight loss...

https://www.vox.com/2016/4/28/11518804/weight-loss-exercise-myth-burn-calories

Why you shouldn't exercise to lose weight, explained with 60+ studies

Oh look, another "You're Doing It Wrong" article! - or is it?

"I'm going to make you work hard," a blonde and perfectly muscled fitness instructor screamed at me in a recent spinning class, "so you can have that second drink at happy hour!"

Remember yesterday when I said I wouldn't be caught dead in a spin(ning) class? This reinforces that.

Anyway, the article dives into some science, much of which could stand to be replicated or at least extended. When it comes to nutrition (or, in this case, exercise) science, I approach it with a healthy (pun intended, as always) dose of skepticism.

And I'm not going to quote a lot from it. Instead, I'm just going to summarize:

Exercise is good (and necessary), but it probably isn't enough, on its own, for losing weight.

This tracks with my own experience, but of course my own experience is a data point of one and when it comes to fitness, I always find out later I've been lying to myself. So I don't trust my own experience, either.

Still, it was true for me that diet alone, without additional exercise (that is, more than what it takes to walk from the couch to the bathroom and back again a few times a day) doesn't work. It requires both.

So what's the point of exercise? I ask myself that every time I get on the elliptical trainer, and I have to remind myself that it makes me feel less dumb and helps fend off depression. That alone is usually reason enough to keep going; any weight loss benefits are icing on the donut. Mmmmm... donut... *drool*

Ahem. Anyway. That works for me until it doesn't, and then I get back into the funk of "I'm depressed." "I should exercise." "I don't feel like it." "But it'll make you feel better." "I don't want to feel better." "But I hate being like this." "So? Shut up and have another bottle of tequila."

Yes, I talk to myself like that when I'm depressed. Does it help? No.

This article, to get back to the point, still doesn't address the question I had yesterday: So what happens if I reach my goal weight?

I mean, this can't be a fully linear process, can it? Like, say you're losing a pound a week. Just as an example. Somehow, you manage to do this regularly and consistently. But there's got to be a limit, right? Else you waste away to nothing (which, now I think of it, would make an excellent story- shit, Stephen King already did it). You keep eating less and less and exercising more and more, in order to keep that pound-a-week thing going, and at some point, it turns into the Red Queen's Race - it takes all your energy just to stand still.

That's what worries me, if I'm being honest. That there's no end to this self-deprivation; that I'm consigned to a lifetime of gray purgatory. They say success requires a lifestyle change, and while I'm perfectly okay with some lifestyle changes, especially if I know that I can relax at some point... some things just aren't worth the rewards.

It's frustrating, really.

3 Like • Comment

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